Question

The area of a rectangle gets reduced by 9 square units, if its length is
reduced by 5 units and the breadth is increased by 3 units. The area is
increased by 67 square units if length is increased by 3 units and breadth is
increased by 2 units. Find the perimeter of the rectangle. [CBSE 2012]
​

Answer 1

Answer:

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Answer 2

Answer:

Perimeter of rectangle = 52 m

Step-by-step explanation:

Let length = x m

Let breadth = y m

Area = xy m²

ATQ:-

Case1:-

Length = (x-5)m

Breadth = (y+3)m

Area = (x-5) (y+3)

ATQ:- (x-5) (y+3) = xy - 9 ----(1)

Also,

Length = (x+3)

Breadth = (y+2)

Area = (x+3) (y+2)

ATQ:-

(x+3) (y+2) = xy + 67 ----(2)

Solve equation (1) and (2)

From equation 1:-

(x-5) (y+3) = xy - 9

xy + 3x - 5y - 15 = xy - 9

3x - 5y = -9 + 15

3x - 5y = 6 ------(3)

Now, solve equation 2

(x+3) (y+2) = xy + 67

xy + 2x + 3y + 6 = xy + 67

2x + 3y = 67 - 6

2x + 3y = 61 ----(4)

Multiply equation (3) with 2 and equation (4) with 3

We get,

6x - 10y = 12 ----(5)

6x + 9y = 183 ----(6)

Subtract equation (5) and (6)

6x - 10y = 12

6x + 9y = 183

- - -

___________

0x - 19y = - 171

___________

-19 y = -171

y = 9

Put y in equation 3

3x - 5y = 6

3x - 5(9) = 6

3x - 45 = 6

3x = 45+6

3x = 51

x = ⁵¹/3

x = 17

So, we get x= 17 and y = 9

Hence, length = 17 m

Breadth = 9 m

Perimeter of rectangle = 2(l+b)

= 2(17+9)m

= 2(26)m

= 52 m